where \(F[p_n]\)  and \(V[p_n]\)  are the Fisher information [1]}, [2]} and the variance of the Rakhmanov density \(\rho _n(x)\)  associated to \(p_n(x)\) , which are defined as

F[pn]= ['n(x)]2n(x)dx,   and   V[pn]=(x)2=x2 -x 2,

respectively, with the expectation value \(\langle x^k \rangle = \int _{\Lambda } x^k \rho _n(x) dx\)  for \(k=1,2\) . Then, the Cramér-Rao complexity quantifies the gradient content (so, the pointwise concentration of the Rakhmanov probability over its support interval) of \(\rho _n(x)\)  jointly with the spreading of the probability around the centroid.
